Related papers: Misere quotients for impartial games

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…

This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and…

Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game…

In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-field-type equilibrium can be characterized by the existence of a multiplier process…

This paper develops and analyses a novel quantum combinatorial game: quantum checkers (codenamed Cheqqers). The concepts of superposition, entanglement, measurements and interference from quantum mechanics are integrated into the game of…

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…

Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…

We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…

Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these…

We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over…

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the…

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…

We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…

This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…

In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is…